Employees who take care of children, parents or other family members should have the right to at least ask for a flexible work schedule, the San Francisco Board of Supervisors unanimously agreed Tuesday.

The vote means that board President David Chiu's legislation - which would require employers in San Francisco to consider workers' requests for flexible hours, telecommuting, job-sharing or other changes to accommodate caregiving - will almost certainly become law. Mayor Ed Lee has said he will sign the bill, which would apply only to businesses with 20 or more employees and would allow employers to reject the request if they had a "good faith business reason" for doing so.

Chiu said the measure will "help workers struggling to be good employees as well as good parents and caregivers."

Although the business community did not support the proposal - the San Francisco Chamber of Commerce stayed neutral - supporters believe the legislation will help both workers and employers. They cite positive experiences with flexible work schedules in other countries, including Britain and Australia, and studies showing that these sorts of arrangements help businesses recruit and retain workers, reduce absenteeism and increase productivity.

"I hope this legislation will nudge real changes in workplace culture and eliminate stigma and bias around workers who request flexible schedules," Chiu said, adding that the city will have to educate businesses and workers about their rights under the measure.

Changing the culture was a big impetus for the law. Initially, Chiu and family advocates had hoped to make the legislation a ballot measure, arguing that it would help spark a conversation and noting that men especially are reticent to ask for family-friendly accommodations because they are afraid of looking uncommitted to work.

But after pushback from the business community and mayor, Chiu negotiated a deal to keep it off the fall ballot while securing Lee's support.

Supervisor Eric Mar said he hopes the legislation is just the beginning of a conversation about how to help families thrive.

"We talk a lot about how unfriendly San Francisco is to families," he said. "This is an excellent first step toward supporting working parents."